# 7.20: Untitled Page 165

## Chapter 7

and the yield of ethylene oxide is 50% ( Y  0 . 50 ) . All of the oxygen in the feed reacts, thus there is no oxygen in Stream #3. The reactor effluent is sent to an absorber where all the ethylene oxide is absorbed in the water entering in Stream #8. Water is fed to the absorber such that ( M

)  100 ( M

) and we assume that all the water leaves the

H2O 8

C2H4O 7

absorber in Stream #7. A portion of Stream #4 is recycled in Stream #5 and a portion is purged in Stream #6. In this example we want to determine the fraction of M

 that needs to be purged in order that 100 mol/h of 4

ethylene oxide are produced by the reactor.

We begin this example by constructing the equations containing information that is either given or required. To be specific, we want to determine the parameter  defined by

M

  M

(1)

6

4

when 100 mol/h of ethylene oxide are produced by the reactor. We represent this information as

R

  ,

  100 mol/h

(2)

C2H4O

We are also given information about the conversion and yield (see Eqs. 7‐8

and 7‐13) that we express as

 RC H

2

4

C  Conversion of ethylene 

 0 7

. 0

(3)

( M

)

C2H4 2

RC H O

Y  Yield of C H O /C H

 0 . 50

(4)

2

4

2

4 

2 4

 RC H

2 4

Other information concerning this process becomes clear when we consider the problem of constructing control volumes for the application of Axiom I. On the basis of the rules for constructing control volumes given at the beginning of this section, we make the following primary cuts of the streams indicated in Figure 7.6a:

I. A cut of Stream #1 is made because information concerning the composition of Stream #1 is given. NOTE: “The feed stream, Stream #1, consists of ethylene ( C H ) and air ( N and O ) .”

2

4

2

2

Material Balances for Complex Systems

307

II. A cut of Stream #2 is made because a constraint on the composition is given. NOTE: “…the mole fraction of ethylene in Stream #2 leaving the mixer must be maintained at 0 . 05 for satisfactory catalyst operation.”

III. One might make a cut of Stream #3 because a constraint on the composition is given. NOTE: “All of the oxygen in the feed reacts, thus there is no oxygen in Stream #3.” However, there are other interpretations of the original statement. For example one could say that since all of the oxygen in the feed reacts, there is no oxygen in Stream #4 and in Stream #7. In addition, one could say that the molar flow rate of oxygen in Stream #2 is equal to the molar rate of consumption of oxygen in the reactor, i.e., 

( M

)   R

. If we

O2 2

O2

choose the second of these three possibilities, there is no need to cut Stream #3, thus we do not make a cut of Stream #3.

IV. The reactor is enclosed in a control volume because volumetric information about the reactor is given. NOTE: “The conversion of ethylene in the reactor is optimized to be 70% ( C  0 . 70 ) and the yield of ethylene oxide is 50% ( Y  0 . 50 ) .”

V. Cuts of Stream #4 and Stream #6 are made because the operating characteristics of the splitter are required. NOTE: “In this example we want to determine the fraction of M

 that needs to be purged in

4

order that 100 mol/h of ethylene oxide are produced by the reactor.”

VI. A cut of Stream #7 is made because information is required, NOTE: “In this example we want to determine the fraction of M

 that

4

needs to be purged in order that 100 mol/h of ethylene oxide are produced by the reactor.”

VII. A cut of Stream #8 is made because information is given. NOTE:

“Water is fed to the absorber such that ( M

)  100 ( M

) .”

H2O 8

C2H O 7

4

The information identified in II and IV can be expressed as ( x

)

  ,

  0 . 05

(5)

C2H4 2

( M

)

  ( M

) ,

  100

(6)

H2O 8

C2H4O 7

308